The flute is a member of the woodwind family (see Figure 1).  A player blows air across the hole in the side of the head joint, which causes air flow patterns at the edge of the lip plate to alternate rapidly.  The alternation causes the air in the tube to resonate.  Waves reflect back and forth in the column of air, creating the tone of the flute.  The lowest note can be played when all the tone holes are closed and the column is at its maximum length.  Opening the tone holes starting at the open end effectively shortens the column.
     The sound of a musical instrument consists of a fundamental frequency plus other higher frequencies (overtones) that form the harmonic series.  The overtones are multiples of the fundamental frequency.  If f is the fundamental, the overtones are 2f, 3f, 4f, 5f, etc.  Each instrument has a unique sound depending on how much of the other frequencies are present in each note.  Although people have different perceptions of a good sound, a full sound is generally one that has a lot of overtones.  A listener can hear a difference between sounds with and without overtones.  A sound is sometimes called tinny if it has a lot of the higher overtones, and it is called mellow if it only consists of the fundamental frequency.  In order to characterize the frequency spectrum of the flute, I took sound samples based on different parameters of several flutes.  In the power spectrum of each sample, I expected to see spikes at the fundamental frequency and at each overtone.  The main focus of this project was A at 440 Hz, but I also took samples of other octaves of A and also of B.  Table 1 shows the first 7 overtones of the harmonic series of A at 440 Hz and the corresponding notes for each overtone.
 

    My goal was to determine if there were patterns in the power spectrums, possibly depending on the flute, the player, or both.

Abstract
Introduction
Experimental Setup
Results
Discussion
Conclusions
References